We have designed an experiment (a pull-out program to improve reading achievement) where (1) schools are randomly assigned to one of four interventions and (2) eligible students within schools are randomly assigned to either a treatment group or a control group. It has been several years since I have used MPLUS and I wanted to see if I could use it to estimate impacts with the following conditions: (1) unequal sample selection probabilities for schools and students (in to interventions and treatment conditions), (2) noncompliance (not all students randomly assigned to treatment actually participated, unequal intervals among test administrations (3 times in year 1 and then once in year 2 and once in year 3). We will want to obtain estimates for both ITT and TOT.

As further analysis, we will want to assess how levels of fidelity (was the intervention delivered the one outlined by the deveoloper), and differences in teacher characteristics affect the observed treatment impact. As an aside, there is no variation within schools in teacher characteristics.

Interesting study. Here are brief answers to your questions. (1) In general this should work fine in Mplus Version 3, see the new Mplus Web Note #8 (and 7) on sampling weights by Asparouhov at the top of the Mplus home page, showing some of the complexities. (2) This fits in with CACE modeling using mixtures and the newer CACE literature for cluster samples, so this can be approached via the new multilevel mixture modeling in Mplus Version 3, where the latent class variable of compliance varies across students but accounts for cluster effects (Booil Jo at booil@stanford.edu and I are currently looking at methodology of related modeling). The multilevel mixture modeling allows predictors on different levels as in regular multilevel modeling.